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baily106
Course Students
 
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Official Guide - p. 114, q 7, powers of 2

by baily106 Sun Jun 08, 2014 7:31 pm

I was looking at the explanation of #7 on page 114, and the question I have is that in determining which quantity is larger Quantity A being 2raised to the 30 minus 2 raised to the 29 all of which is divided by 2 vice Quantity B which is simply 2 raised to the 28. In step two, why do you subtract 2 raised to the 29 from both sides when you can simply subtract 29 from 30 since they have the same base? In that case can't you say it is 2 raised to the 1 and that it is less than 2 raised to the 29?

Thanks,
Anisha
tommywallach
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Re: Official Guide Book Question

by tommywallach Mon Jun 09, 2014 11:32 pm

Anisha,

Please, if you're going to ask about questions, write the question first, so that people can see it if they don't have the book on them.

Quantity A: (2 ^ 30 - 2 ^ 29) / 2
Quantity B: 2 ^ 28

Your mistake is thinking you can subtract powers when subtracting two terms with the same base. You only subtract powers when dividing:

2^30 / 2^29 = 2^1

You do not subtract powers when subtracting two terms with the same base.

This means you simply must divide the two into the two terms:

2^30/2 - 2^29/2 = 2^29 - 2^28

Then, factor out the largest common term, which is 2^28:

2^28 (2 - 1) = 2 ^ 28

So the answer is C.

-t
baily106
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Posts: 49
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Re: Official Guide - p. 114, q 7, powers of 2

by baily106 Tue Jun 10, 2014 2:15 pm

Thanks T for the answer and also rewriting the titles on my recent posts.

I understand up until the last part on this particular question.
You state that you factor out the largest common term, got it.
So you have 2^28(2-1) = 2^28
How can they be equal though? Don't you have to take the (2-1) into consideration?

Thanks.
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Official Guide - p. 114, q 7, powers of 2

by tommywallach Fri Jun 13, 2014 2:44 pm

Hey Anisha,

Of course! But 2-1 = 1, and 1 * 2^28 = 2^28.

Tada!

-t